Refined crustal and uppermost mantle structure of southern California by ambient noise adjoint tomography

Three‐Dimensional Sensitivity Kernels for Multicomponent Empirical Green's Functions From Ambient Noise: Methodology and Application to Adjoint Tomography

“…Let I = J = Z in equation , then we have which suggests that the individual kernel for Z‐Z component EGFs can be constructed from the interaction of the forward field from a Delta‐function vertical point force at x s and the adjoint field due to an adjoint source time function f ZZ injected at the receiver in the vertical direction. Equation shows exactly how sensitivity kernels are computed in Rayleigh‐wave type ANAT (e.g., Chen et al, ; Wang et al, ). The adjoint source f ZZ is constructed from the measurement made between the Z‐Z component EGF and the corresponding SGF at the receiver.…”

“…All numerical simulations are conducted using an open‐source package SPECFEM3D based on SEM (https://github.com/geodynamics/specfem3d) for a 3‐D southern California velocity model constructed by Wang et al () based on Rayleigh wave ANAT. The mesh used for the numerical simulations is the same as that described in Wang et al () with the accuracy down to a period of 2 s. Throughout this section, we construct multitaper traveltime misfit kernels (Laske & Masters, ; Tape et al, ; Zhou et al, ) between a source (CI.STC) and a number of receivers (Figure c) for T‐T and R‐R component measurements made between EGFs and SGFs. For the purpose of benchmarking, we first perform forward and adjoint simulations by placing point‐force sources in the transverse and radial directions to construct the reference SGFs, individual, and event kernels.…”

“…In our previous study (Wang et al, ), vertical‐component ambient noise data are processed to obtain Z‐Z component Rayleigh wave EGFs, which are utilized to iteratively improve the earthquake‐based adjoint tomographic model M16 of southern California (Tape et al, , ). In this study, we extract T‐T component NCFs from ambient seismic noise recorded at the 148 stations in southern California (Figure ) from 2006 to 2012, by processing the north and east component seismograms simultaneously following the three‐component noise data processing procedures described by Lin et al ().…”

“…The inversion procedures adopted here are similar to those of Rayleigh‐wave ANAT, as elaborated in Wang et al (). Here, we briefly summarize the inversion iteration procedure with a focus on the Love waves: (1)Forward simulations: For each master station, we conduct two forward simulations with point‐force sources placed in the north and east directions, respectively.…”

“…The adjoint sources of the three period bands at the receiver are added up to form the final adjoint source. (3)Adjoint simulation: The T‐T component adjoint sources are rotated to the east and north directions and injected simultaneously at all receivers to generate the adjoint fields, which interact with the forward fields to obtain the two rotated event kernels, respectively. (4)Postprocessing: Rotated event kernels for all master stations are summed, preconditioned, and smoothed to obtain the final misfit gradient. The scale lengths of the Gaussian function used for smoothing are the same as those in the Rayleigh‐wave ANAT study (Wang et al, ). (5)Line search: The optimal step length for the model update is determined based on the line search of a representative subset of 19 master stations (red triangles in Figure ) distributed almost evenly throughout the study region, following the practice in many other adjoint tomography studies (e.g., Chen et al, ; Zhu et al, ). (6)Model update: A new model is obtained using the optimal step length. If the corresponding misfit reduction from last iteration is less than or equal to 3%, the iteration ends; otherwise, the next iteration starts by going back to step 1.…”